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Quantitative stability for the first Dirichlet eigenvalue in Reifenberg flat domains in

✍ Scribed by Antoine Lemenant; Emmanouil Milakis

Book ID
108178581
Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
227 KB
Volume
364
Category
Article
ISSN
0022-247X

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We studied the two known works on stability for isoperimetric inequalities of the first eigenvalue of the Laplacian. The earliest work is due to A. Melas who proved the stability of the Faber-Krahn inequality: for a convex domain contained in n with Ξ» close to Ξ», the first eigenvalue of the ball B o

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## Abstract For certain unbounded domains the Laplace operator with Dirichlet condition is shown to have an unbounded sequence of eigenvalues which are embedded into the essential spectrum. A typical example of such a domain is a locally perturbed cylinder with circular cross‐section whose diameter